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1. (x,y,z) --> (x,y,-z) [ 1 0 0 ] [ 0 1 0 ] [ 0 0 -1 ] 2.(x,y,z) --> (-y, x, z) [ 0 -1 0 ] [ 1 0 0 ] [ 0 0 -1 ] 3. (x,y,z) --> (3x, 3y, 3z) [ 3 0 0 ] [ 0 3 0 ] [ 0 0 3 ] 4. (x,y, z) --> (2x-y-z, 2y-x-z, 2z-x-y)/3 [ 2/3 -1/3 -1/3 ] [ -1/3 2/3 -1/3 ] [ -1/3 -1/3 2/3 ] 5. (x,y,z) --> (x+y+z, x+y+z, x+y+z)/3 [ 1/3 1/3 1/3...

粗體紅字表向量 Q1: 設 u=(1,1,1), v=(-1, 0, 2), w=(1, 4, 3) 求w在u, v形成平面之分向量 au+bv即可 即 w-au-bv 與 u, v均垂直(內積=0), 則 (w- au -bv)•u=0 => 8-3a-b=0 (w- au -bv)•v=0 => 5-a-5b=0 聯立得 (a,b)=(5/2, 1/2) 故最近之點(向量)為 au+bv=(2, 5/2, 7/2) Q2: (高中作法) 設P(a,b,c), 平面...